Решебник по геометрии 9 класс Мерзляк Задание 266

\[Схематический\ рисунок.\]

\[Дано:\]

\[AB = 5\sqrt{3}\ см;\]

\[\angle A = 35{^\circ};\]

\[\angle B = 25{^\circ}.\]

\[Найти:\]

\[\cup AB;\ \]

\[\cup BC;\]

\[\cup AC.\]

\[Решение.\]

\[1)\ В\ \mathrm{\Delta}ABC:\]

\[\angle C = 180{^\circ} - \angle A - \angle B = 120{^\circ};\]

\[R = \frac{\text{AB}}{2\sin{\angle C}} = \frac{5\sqrt{3}}{2\sin{120{^\circ}}} = 5.\]

\[2)\ Окружность:\]

\[C = 2\pi R = 2\pi \bullet 5 = 10\pi;\]

\[\cup AB = 2 \bullet 10\pi \bullet \frac{120{^\circ}}{360{^\circ}} = \frac{20\pi}{3};\]

\[\cup BC = 2 \bullet 10\pi \bullet \frac{35{^\circ}}{360{^\circ}} = \frac{35\pi}{18};\]

\[\cup AC = 2 \bullet 10\pi \bullet \frac{25{^\circ}}{360{^\circ}} = \frac{25\pi}{18}.\]

\[Ответ:\ \frac{20\pi}{3}\ см;\ \frac{35\pi}{18}\ см;\ \frac{25\pi}{18}\ см.\]